sqrtLCat

sqrtLCat is a software library and reference implementation that provides algorithms for computing square roots for integers and floating-point values. It is designed to balance speed, accuracy, and portability across platforms, with a focus on embedded and performance-sensitive environments.

Features include exact integer square roots, IEEE-754 compliant floating-point sqrt, and configurable approximate methods with user-selectable error bounds. The library offers multiple precision modes, supports 32-bit and 64-bit integers, and includes fixed-point variants for systems without floating-point units. It is implemented in C and C++, with bindings available for other languages through foreign function interfaces. The codebase emphasizes a small runtime footprint and optional SIMD-accelerated paths on modern CPUs.

Implementation details: sqrtLCat uses a two-stage approach for real inputs—an inexpensive initial estimate obtained from look-up tables or bit-level techniques, followed by a small fixed number of Newton-Raphson iterations to refine the result. It also provides vectorized sqrt operations on platforms with SIMD support and handles edge cases such as negative inputs and NaN in a consistent manner.

Origin and licensing: sqrtLCat originated as an open-source project developed by a community of contributors and released under a permissive license. The project maintains a public repository with issue tracking, documentation, and release notes.

Usage and impact: adopted by several open-source graphics engines, scientific libraries, and educational resources as a dependable implementation of square-root functionality. It serves as a reference for comparing alternative square-root algorithms and for teaching numerical methods.

See also: numerical analysis, square root algorithms, fixed-point arithmetic, floating-point arithmetic.